3

docx

School

California State University, Monterey Bay *

*We aren’t endorsed by this school

Course

1281

Subject

Mathematics

Date

Nov 24, 2024

Type

docx

Pages

Uploaded by WESIMBEH

MATH 1281 Discussion Forum Unit 4 Statistical Inference on HIV/AIDS T-distribution is a probability function that is useful for us to estimate population parameters from small sample sizes. This is useful to help us predict the population standard deviation (which we often don’t know) using the sample standard deviation as an estimate (Dies et al., 2019). We could conduct two t-distribution tests involving paired and unpaired data to investigate the field of human immunodeficiency virus (HIV) and acquired immunodeficiency syndrome (AIDS). Evaluating the association between two observations using t-tests could be conducted using paired and unpaired data. To be diagnosed with AIDS, an individual has to have less than 200 CD4 cells per microliter of blood (“HIV/AIDS Diagnosis,” n.d.). Therefore, in an example of paired data, we could measure the average number of CD4 cells per microliter of blood immediately after 30 individuals’ diagnosis of AIDS and compare it to the average number of CD4 cells per microliter of blood three months after their diagnosis. In an example of unpaired data, we could evaluate 30 individuals diagnosed with HIV who have been taking highly active antiretroviral therapy (HAART) for one month to determine the average number of individuals who have 200 copies/ml blood of the human immunodeficiency virus or less. While both examples pertain to the same field of interest, they differ significantly. Paired data exists when there is a correspondence or relationship between two sets of observations. This often means that the data is dependent on each other. This includes investigations in which the same sampled individuals are repeatedly measured (Dies et al., 2019). The above example of paired data illustrates this. We are investigating the same individual twice after three months. This indicates dependency because their initial CD4 cell count will likely affect their CD4 cell count measured three months later. Contrastingly, unpaired data exists when there is no relationship between two sets of observations. These observations are independent of each other. In these cases, we are investigating whether there is a difference between the two independent observations (Dies et al., 2019). The above example of unpaired data illustrates this. In the sample of individuals who have taken HAART for one month, they can only be classified as having 200 copies/ml of blood or less, or more than 200 copies/ml of blood. They cannot exist in both categories simultaneously, indicating independence. These paired and unpaired data examples illustrate the differences between dependency and independence. We must use a one-sample t-test for our paired data and a two-sample t-test for our unpaired data. In the example of our paired data, we could investigate the difference between CD4 cells per microliter of blood immediately after their AIDS diagnosis and that three months later. In other words, we would subtract the average CD4 cell count after three months from that immediately after their diagnosis. This would give us a sample mean and standard deviation of

the differences. Because we are only interested in the sample differences, we would conduct a one-sample t-test using these statistics. In the example of our unpaired data, we could investigate whether there is a difference in the number of copies/ml of blood in 30 HIV patients who have taken HAART for a month. Because we are comparing the average number of individuals with 200 copies/ml of blood or less to that of individuals with more than 200 copies/ml of blood, we would conduct a two-sample t-test. We are interested in determining whether the means of the two independent sample populations are different. Therefore, we conduct a one-sample t-test for paired data and a two-sample t-test for unpaired data. Words: 592 References: Dies, D. M., Barr, C. D., & Çetinkaya-R, M. (2019). Openintro statistics – Fourth edition: Chapters 7.1, 7.2, & 7.3 . Open Textbook Library. [PDF]. https://www.biostat.jhsph.edu/~iruczins/teaching/books/2019.openintro.statistics.pdf . HIV/AIDS Diagnosis . (n.d.). Stanford Medicine: Health Care. https://stanfordhealthcare.org/medical-conditions/sexual-and-reproductive-health/hiv- aids/diagnosis.html#:~:text=Tests%20for%20AIDS&text=It%20is%20diagnosed%20if %20the,who%20have%20weakened%20immune%20systems .

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

3

Related Documents